Nursing Elites

1. Solve the equation 8x − 6 = 3x + 24. Which of the following is the correct solution?

• A. x = 2.5
• B. x = 3.6
• C. x = 5
• D. x = 6

Correct answer: D

Rationale: To solve the equation 8x − 6 = 3x + 24, start by adding 6 to both sides: 8x − 6 + 6 = 3x + 24 + 6, which simplifies to 8x = 3x + 30. Next, subtract 3x from both sides to get 5x = 30. Finally, divide both sides by 5 to solve for x: x = 6. Therefore, the correct solution is x = 6. Choices A, B, and C are incorrect because they do not result from the correct algebraic manipulation of the equation.

2. Using the chart below, which equation describes the relationship between x and y?

• A. x = 3y
• B. y = 3x
• C. y = 1/3x
• D. x/y = 3

Correct answer: B

Rationale: The correct equation that describes the relationship between x and y based on the chart is y = 3x. This is because each y-value in the chart is 3 times the x-value. Choice A (x = 3y) is incorrect as it implies x is 3 times y, which is the opposite of the relationship shown in the chart. Choice C (y = 1/3x) is incorrect since the relationship in the chart indicates y is 3 times x, not a third of x. Choice D (x/y = 3) is incorrect as it represents a ratio between x and y equal to 3, which is not in line with the relationship depicted in the chart.

3. Solve |x| = 10.

• A. -10, 10
• B. -11, 11
• C. -12, 12
• D. -13, 13

Correct answer: A

Rationale: The absolute value of x is equal to 10 when x is either -10 or 10. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not satisfy the equation |x| = 10. For choice B, -11 and 11 do not satisfy the condition. Choices C and D also do not provide solutions that meet the equation's requirement.

4. How many milliliters are there in 3.2 liters?

• A. 0.32
• B. 32
• C. 3200
• D. 320

Correct answer: C

Rationale: To convert liters to milliliters, you need to know that 1 liter is equal to 1000 milliliters. Therefore, 3.2 liters is equivalent to 3.2 x 1000 = 3200 milliliters. Choice A (0.32) is incorrect as it incorrectly moves the decimal point. Choice B (32) is incorrect as it doesn't consider the conversion factor between liters and milliliters. Choice D (320) is incorrect as it is a partial conversion error, missing a zero at the end.

5. A container holds 10 liters of water. If 25% of the water is used, how many liters are left?

• A. 7.5 liters
• B. 8 liters
• C. 6.5 liters
• D. 8.5 liters

Correct answer: A

Rationale: To find the amount of water left after 25% is used, you need to calculate 75% of the total water. 75% of 10 liters is 7.5 liters, which means that 7.5 liters of water are left. Therefore, the correct answer is A. Choice B (8 liters) is incorrect because this would be the total water remaining if 20% was used, not 25%. Choice C (6.5 liters) is incorrect as it does not account for the correct percentage of water left. Choice D (8.5 liters) is incorrect as it miscalculates the amount of water remaining after 25% is used.

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